If $B$ is the magnetic Induction, at the centre of a circular coil of radius ‘r’ carrying a current is 1 T, then its value at a distance of $\sqrt{3}$ r on the axis from the centre of the coil is

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$\frac{1}{8} T$

$\frac{1}{16} T$

answer is A.

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Detailed Solution

$\begin{array}{l} B = \frac{μ_{0} i}{2 r}; 1 = \frac{μ_{0} i}{2 r}; μ_{0} i = 2 r \\ B^{1} = \frac{μ_{0} {ir}^{2}}{2 {(r^{2} + x^{2})}^{\frac{3}{2}}} = \frac{2 r \times r^{2}}{2 {[r^{2} + 3 r^{2}]}^{\frac{3}{2}}} = \frac{1}{8} T \end{array}$

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